Topology and strong four fermion interactions in four dimensions
We study massless fermions interacting through a particular four-fermion term in four dimensions. Exact symmetries prevent the generation of bilinear fermion mass terms. We determine the structure of the low-energy effective action for the auxiliary field needed to generate the four-fermion term and find it has an novel structure that admits topologically nontrivial defects with nonzero Hopf invariant. We show that fermions propagating in such a background pick up a mass without breaking symmetries. Furthermore, pairs of such defects experience a logarithmic interaction. We argue that a phase transition separates a phase where these defects proliferate from a broken phase where they are bound tightly. We conjecture that, by tuning one additional operator, the broken phase can be eliminated with a single BKT-like phase transition separating the massless from massive phases.
- Research Organization:
- Syracuse Univ., NY (United States)
- Sponsoring Organization:
- USDOE Office of Science (SC), High Energy Physics (HEP)
- Grant/Contract Number:
- SC0009998
- OSTI ID:
- 1436213
- Alternate ID(s):
- OSTI ID: 1498878
- Journal Information:
- Physical Review D, Journal Name: Physical Review D Vol. 97 Journal Issue: 9; ISSN 2470-0010
- Publisher:
- American Physical SocietyCopyright Statement
- Country of Publication:
- United States
- Language:
- English
Web of Science
Why is the mission impossible? Decoupling the mirror Ginsparg–Wilson fermions in the lattice models for two-dimensional Abelian chiral gauge theories
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journal | July 2019 |
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